Finite Group Databasebeta

← #11773307

Subgroups — #11773307

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C22×#3722C211yesmaximal, characteristic
4C22×#3722C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#71570—31nomaximal
9#69428—31nomaximal
10C24×C3⋊D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3752—22no—
18C2×#3752—22no—
19C2×#3752—22no—
20C2×C3×Dic3⋊C4—22no—
21C2×C3×Dic3⋊C4—22no—
22C2×C3×Dic3⋊C4—22no—
23C2×#3722—22no—
24C2×#3722—22no—
25C2×#3722—22no—
26C2×#3722—22no—
27C2×#3722—22no—
28C2×#3722C414yescomplemented
29C3×C3⋊#95—22no—
30#63579—22no—
31#63579—22no—
32C22×C3×C4⋊C4—31no—
33C22×(C2×D3)⋊C4—31no—
34C22×(C2×D3)⋊C4—31no—
35C22×(C2×D3)⋊C4—31no—
36C22×(C2×D3)⋊C4—31no—
37C22×(C2×D3)⋊C4—31no—
38C22×(C2×D3)⋊C4—31no—
39C22×(C2×D3)⋊C4—61no—
40C22×Dic3⋊C4D311yescharacteristic, complemented
41C2×C3×#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95D311yescharacteristic, complemented
47C24×C32C2311yescharacteristic
48C23×C3⋊D3—21no—
49C23×C3⋊D3—21no—
50C23×C3⋊D3—21no—
51C23×C3⋊D3—21no—
52C23×C3⋊D3—21no—
53C23×C3⋊D3—21no—
54C23×C3⋊D3—21no—
55C23×C3⋊D3—21no—
56C23×C3⋊D3—21no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3—21no—
59C23×C3⋊D3—21no—
60C23×C3⋊D3C2×C412yes—
61C23×C3⋊D3D412yes—
62C23×C3⋊D3Q812yes—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4D412yes—
70C22×C3⋊Dic3—21no—
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3D412yes—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3C2×C412yes—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105#3752—28no—
106C3×Dic3⋊C4—28no—
107#3722—28no—
108#3722—28no—
109#1439—91noSylow
110C24×D3—31no—
111C24×D3—31no—
112C24×D3—61no—
113C23×C3×C4—21no—
114C23×C3×C4—31no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×C3×C4—31no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C2×D311yescharacteristic
120C23×Dic3—31no—
121C23×Dic3—31no—
122C23×Dic3—61no—
123C23×Dic3C2×D311yescharacteristic
124C23×Dic3C2×D311yescharacteristic
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C2×C3×C4⋊C4—62no—
128C2×C3×C4⋊C4—62no—
129C2×C3×C4⋊C4—62no—
130C2×(C2×D3)⋊C4—34no—
131C2×(C2×D3)⋊C4—34no—
132C2×(C2×D3)⋊C4—62no—
133C2×(C2×D3)⋊C4—62no—
134C2×(C2×D3)⋊C4—62no—
135C2×(C2×D3)⋊C4—62no—
136C2×(C2×D3)⋊C4—62no—
137C2×(C2×D3)⋊C4—62no—
138C2×(C2×D3)⋊C4—62no—
139C2×(C2×D3)⋊C4—62no—
140C2×(C2×D3)⋊C4—62no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4—64no—
143C2×(C2×D3)⋊C4—64no—
144C2×(C2×D3)⋊C4—64no—
145C2×(C2×D3)⋊C4—62no—
146C2×(C2×D3)⋊C4—62no—
147C2×(C2×D3)⋊C4—62no—
148C2×(C2×D3)⋊C4—62no—
149C2×(C2×D3)⋊C4—62no—
150C2×(C2×D3)⋊C4—62no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C3×#95—62no—
155C3⋊#95—22no—
156C3⋊#95—62no—
157C3⋊#95—62no—
158C3⋊#95—62no—
159C3⋊#95—62no—
160C23×C32C22×C411yescharacteristic
161C23×C32C2×D411yescharacteristic
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C23×C32C2×D411yescharacteristic
166C23×C32C2×D411yescharacteristic
167C23×C32C2×D411yescharacteristic
168C23×C32C2×Q811yescharacteristic
169C23×C32#4111yescharacteristic
170C23×C32#4111yescharacteristic
171C23×C32#4111yescharacteristic
172C23×C32#4111yescharacteristic
173C23×C32#4111yescharacteristic
174C23×C32#4111yescharacteristic
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3—22no—
184C22×C3⋊D3—22no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—22no—
188C22×C3⋊D3—22no—
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3—22no—
193C22×C3⋊D3—41no—
194C22×C3⋊D3—41no—
195C22×C3⋊D3—41no—
196C22×C3⋊D3—41no—
197C22×C3⋊D3—41no—
198C22×C3⋊D3—41no—
199C22×C3⋊D3—41no—
200C22×C3⋊D3—41no—
201C22×C3⋊D3—41no—
202C22×C3⋊D3—41no—
203C22×C3⋊D3—41no—
204C22×C3⋊D3—41no—
205C22×C3⋊D3—41no—
206C22×C3⋊D3—41no—
207C22×C3⋊D3—41no—
208C22×C3⋊D3—41no—
209C22×C3⋊D3C4⋊C414yescomplemented
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4—41no—
216C2×C32×C4—41no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—41no—
221C2×C3⋊Dic3—41no—
222C2×C3⋊Dic3—41no—
223C2×C3⋊Dic3—41no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—41no—
244C2×C3×Dic3—41no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3—41no—
250C2×C3×Dic3—41no—
251C2×C3×Dic3C22⋊C414yescomplemented
252C22×C4⋊C4—31no—
253C22×C22⋊C4—91no—
254C22×C22⋊C4—91no—
255C22×C22⋊C4—91no—
256C2×#95—31no—
257C2×#95—91no—
258C2×#95—91no—
259C24×C3—21no—
260C24×C3C22×D311yescharacteristic
261C24×C3C22×D311yescharacteristic
262C23×D3—32no—
263C23×D3—32no—
264C23×D3—32no—
265C23×D3—32no—
266C23×D3—32no—
267C23×D3—32no—
268C23×D3—62no—
269C23×D3—62no—
270C23×D3—62no—
271C23×D3—62no—
272C23×D3—62no—
273C23×D3—62no—
274C23×D3—62no—
275C23×D3—61no—
276C23×D3—61no—
277C23×D3—61no—
278C23×D3—61no—
279C23×D3—61no—
280C23×D3—61no—
281C23×D3—61no—
282C23×D3—61no—
283C23×D3—61no—
284C23×D3—61no—
285C23×D3—61no—
286C23×D3—61no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—61no—
290C23×D3—61no—
291C23×D3—61no—
292C23×D3—61no—
293C23×D3—61no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—121no—
300C23×D3—121no—
301C23×D3—121no—
302C23×D3—121no—
303C23×D3—121no—
304C23×D3—121no—
305C23×D3—121no—
306C23×D3—121no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—22no—
322C22×C3×C4—32no—
323C22×C3×C4—32no—
324C22×C3×C4—32no—
325C22×C3×C4—32no—
326C22×C3×C4—32no—
327C22×C3×C4—32no—
328C22×C3×C4—41no—
329C22×C3×C4—41no—
330C22×C3×C4—41no—
331C22×C3×C4—41no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4D1212yes—
355C22×C3×C4#6712yes—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—32no—
379C22×Dic3—32no—
380C22×Dic3—62no—
381C22×Dic3—62no—
382C22×Dic3—62no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—121no—
396C22×Dic3—121no—
397C22×Dic3—121no—
398C22×Dic3—121no—
399C22×Dic3C4×D312yes—
400C22×Dic3C4×D312yes—
401C22×Dic3D1212yes—
402C22×Dic3#6712yes—
403C22×Dic3#6712yes—
404C22×Dic3#6712yes—
405C3×C4⋊C4—68no—
406(C2×D3)⋊C4—68no—
407(C2×D3)⋊C4—68no—
408(C2×D3)⋊C4—68no—
409(C2×D3)⋊C4—616no—
410(C2×D3)⋊C4—68no—
411(C2×D3)⋊C4—68no—
412(C2×D3)⋊C4—68no—
413Dic3⋊C4—28no—
414C22×C32C2×C22⋊C411yescharacteristic
415C22×C32C2×C4⋊C411yescharacteristic
416C22×C32#11711yescharacteristic
417C22×C32C4×D411yescharacteristic
418C22×C32C4×D411yescharacteristic
419C22×C32C4×D411yescharacteristic
420C22×C32C4×D411yescharacteristic
421C22×C32#12011yescharacteristic
422C22×C32#12011yescharacteristic
423C22×C32#12011yescharacteristic
424C22×C32#12111yescharacteristic
425C22×C32#12111yescharacteristic
426C22×C32#12111yescharacteristic
427C22×C32#12111yescharacteristic
428C22×C32#12111yescharacteristic
429C22×C32#12111yescharacteristic
430C22×C32#12111yescharacteristic
431C22×C32#12111yescharacteristic
432C22×C32C22⋊Q811yescharacteristic
433C22×C32C22⋊Q811yescharacteristic
434C22×C32C22⋊Q811yescharacteristic
435C22×C32C22⋊Q811yescharacteristic
436C22×C32C22⋊Q811yescharacteristic
437C22×C32C22⋊Q811yescharacteristic
438C22×C32#12311yescharacteristic
439C22×C32#12311yescharacteristic
440C22×C32#12311yescharacteristic
441C22×C32#12311yescharacteristic
442C22×C32#12311yescharacteristic
443C22×C32#12411yescharacteristic
444C22×C32#12411yescharacteristic
445C22×C32#12411yescharacteristic
446C22×C32#12611yescharacteristic
447C22×C32#12611yescharacteristic
448C22×C32#12711yescharacteristic
449C2×C3⋊D3—24no—
450C2×C3⋊D3—24no—
451C2×C3⋊D3—24no—
452C2×C3⋊D3—42no—
453C2×C3⋊D3—42no—
454C2×C3⋊D3—42no—
455C2×C3⋊D3—42no—
456C2×C3⋊D3—42no—
457C2×C3⋊D3—42no—
458C2×C3⋊D3—42no—
459C2×C3⋊D3—42no—
460C2×C3⋊D3—42no—
461C2×C3⋊D3—42no—
462C2×C3⋊D3—42no—
463C2×C3⋊D3—42no—
464C32×C4—42no—
465C3⋊Dic3—42no—
466C3×Dic3—24no—
467C3×Dic3—42no—
468C3×Dic3—42no—
469C3×Dic3—42no—
470C25—91no—
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—31no—
474C23×C4—31no—
475C23×C4—91no—
476C23×C4D3211yescharacteristic
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C22⋊C4—94no—
481C2×C22⋊C4—182no—
482C2×C22⋊C4—182no—
483C2×C22⋊C4—182no—
484C2×C22⋊C4—182no—
485C2×C22⋊C4—182no—
486C2×C22⋊C4—182no—
487C2×C22⋊C4—182no—
488C2×C22⋊C4—182no—
489#95—62no—
490#95—182no—
491#95—182no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3C2×C4×D311yescharacteristic
508C23×C3C2×C4×D311yescharacteristic
509C23×C3C2×D1211yescharacteristic
510C23×C3C2×D1211yescharacteristic
511C23×C3#23511yescharacteristic
512C23×C3#23511yescharacteristic
513C23×C3#23511yescharacteristic
514C23×C3#23511yescharacteristic
515C23×C3#23511yescharacteristic
516C23×C3#23511yescharacteristic
517C23×C3D3×D411yescharacteristic
518C23×C3D3×D411yescharacteristic
519C23×C3D3×D411yescharacteristic
520C23×C3D3×D411yescharacteristic
521C23×C3D3×D411yescharacteristic
522C23×C3D3×D411yescharacteristic
523C23×C3D3×D411yescharacteristic
524C23×C3D3×D411yescharacteristic
525C23×C3#23711yescharacteristic
526C23×C3#23711yescharacteristic
527C23×C3D3×Q811yescharacteristic
528C23×C3D3×Q811yescharacteristic
529C23×C3#23911yescharacteristic
530C23×C3#23911yescharacteristic
531C23×C3#23911yescharacteristic
532C23×C3#23911yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C23×C3C2×#6711yescharacteristic
535C23×C3C2×#6711yescharacteristic
536C23×C3C2×#6711yescharacteristic
537C22×D3—34no—
538C22×D3—34no—
539C22×D3—64no—
540C22×D3—64no—
541C22×D3—64no—
542C22×D3—64no—
543C22×D3—64no—
544C22×D3—64no—
545C22×D3—64no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—62no—
555C22×D3—62no—
556C22×D3—62no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—62no—
579C22×D3—62no—
580C22×D3—62no—
581C22×D3—62no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—121no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3—121no—
639C22×D3—121no—
640C22×D3—121no—
641C22×D3—121no—
642C2×C3×C4—24no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—34no—
650C2×C3×C4—42no—
651C2×C3×C4—42no—
652C2×C3×C4—42no—
653C2×C3×C4—42no—
654C2×C3×C4—42no—
655C2×C3×C4—42no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—62no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—121no—
680C2×C3×C4—121no—
681C2×C3×C4—121no—
682C2×C3×C4—121no—
683C2×C3×C4—121no—
684C2×C3×C4—121no—
685C2×C3×C4—121no—
686C2×C3×C4—121no—
687C2×C3×C4—121no—
688C2×C3×C4—121no—
689C2×C3×C4—121no—
690C2×C3×C4—121no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—64no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—122no—
726C2×Dic3—122no—
727C2×Dic3—122no—
728C2×Dic3—122no—
729C2×Dic3—122no—
730C2×Dic3—122no—
731C2×Dic3—121no—
732C2×Dic3—121no—
733C2×Dic3—121no—
734C2×Dic3—121no—
735C2×Dic3—121no—
736C2×Dic3—121no—
737C2×Dic3—121no—
738C2×Dic3—121no—
739C2×Dic3(C2×D3)⋊C414yescomplemented
740C2×C32#38011yescharacteristic
741C2×C32#38511yescharacteristic
742C2×C32#38511yescharacteristic
743C2×C32#38611yescharacteristic
744C2×C32#38811yescharacteristic
745C2×C32#38811yescharacteristic
746C2×C32#39011yescharacteristic
747C2×C32#39211yescharacteristic
748C2×C32#39311yescharacteristic
749C2×C32#39411yescharacteristic
750C2×C32#39411yescharacteristic
751C2×C32#39611yescharacteristic
752C2×C32#39611yescharacteristic
753C2×C32#39711yescharacteristic
754C2×C32#39911yescharacteristic
755C3⋊D3—44no—
756C24—92no—
757C24—92no—
758C24—92no—
759C24—181no—
760C24—181no—
761C24—181no—
762C24—181no—
763C24—181no—
764C24—181no—
765C24—181no—
766C24—181no—
767C24—181no—
768C24—181no—
769C24—181no—
770C24—181no—
771C24C2×D3211yescharacteristic
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—32no—
779C22×C4—32no—
780C22×C4—32no—
781C22×C4—32no—
782C22×C4—32no—
783C22×C4—32no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—92no—
807C22×C4—181no—
808C22×C4—181no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4—181no—
812C22×C4—181no—
813C22×C4#62612yes—
814C4⋊C4—68no—
815C22⋊C4—188no—
816C22⋊C4—188no—
817C22⋊C4—188no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3#87211yescharacteristic
854C22×C3C4×D1211yescharacteristic
855C22×C3#87511yescharacteristic
856C22×C3#87611yescharacteristic
857C22×C3D3×C22⋊C411yescharacteristic
858C22×C3#67⋊C411yescharacteristic
859C22×C3#88211yescharacteristic
860C22×C3#88211yescharacteristic
861C22×C3#88311yescharacteristic
862C22×C3#88411yescharacteristic
863C22×C3#88411yescharacteristic
864C22×C3#88411yescharacteristic
865C22×C3#88411yescharacteristic
866C22×C3#88411yescharacteristic
867C22×C3#88511yescharacteristic
868C22×C3#88511yescharacteristic
869C22×C3D3×C4⋊C411yescharacteristic
870C22×C3D3×C4⋊C411yescharacteristic
871C22×C3#89211yescharacteristic
872C22×C3#89311yescharacteristic
873C22×C3#89311yescharacteristic
874C22×C3#89311yescharacteristic
875C22×C3#89411yescharacteristic
876C22×C3#89411yescharacteristic
877C22×C3#89411yescharacteristic
878C22×C3#89411yescharacteristic
879C22×C3#89411yescharacteristic
880C22×C3#89411yescharacteristic
881C22×C3#89411yescharacteristic
882C22×C3#89511yescharacteristic
883C22×C3#89511yescharacteristic
884C22×C3#89511yescharacteristic
885C22×C3#89511yescharacteristic
886C22×C3#89611yescharacteristic
887C22×C3#89611yescharacteristic
888C22×C3#89611yescharacteristic
889C22×C3#89611yescharacteristic
890C22×C3#89611yescharacteristic
891C22×C3#89611yescharacteristic
892C22×C3#89711yescharacteristic
893C22×C3#89711yescharacteristic
894C22×C3#89811yescharacteristic
895C22×C3#89811yescharacteristic
896C22×C3#89811yescharacteristic
897C22×C3C2×(C2×D3)⋊C411yescharacteristic
898C22×C3C4×#6711yescharacteristic
899C22×C3C4×#6711yescharacteristic
900C22×C3C4×#6711yescharacteristic
901C22×C3#92911yescharacteristic
902C22×C3#92911yescharacteristic
903C22×C3#93011yescharacteristic
904C22×C3#93011yescharacteristic
905C22×C3#93011yescharacteristic
906C22×C3#93711yescharacteristic
907C22×C3#93711yescharacteristic
908C22×C3#93711yescharacteristic
909C22×C3#93811yescharacteristic
910C22×C3#93911yescharacteristic
911C22×C3#93911yescharacteristic
912C22×C3#93911yescharacteristic
913C22×C3#94011yescharacteristic
914C22×C3#94011yescharacteristic
915C22×C3#94611yescharacteristic
916C22×C3#94611yescharacteristic
917C22×C3#94611yescharacteristic
918C22×C3#94611yescharacteristic
919C22×C3#94711yescharacteristic
920C22×C3#94711yescharacteristic
921C22×C3#94711yescharacteristic
922C22×C3#95311yescharacteristic
923C2×D3—68no—
924C2×D3—64no—
925C2×D3—64no—
926C2×D3—64no—
927C2×D3—64no—
928C2×D3—64no—
929C2×D3—64no—
930C2×D3—124no—
931C2×D3—124no—
932C2×D3—124no—
933C2×D3—124no—
934C2×D3—124no—
935C2×D3—124no—
936C2×D3—124no—
937C2×D3—124no—
938C2×D3—124no—
939C2×D3—124no—
940C2×D3—124no—
941C2×D3—124no—
942C2×D3—124no—
943C2×D3—124no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—122no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—122no—
955C2×D3—122no—
956C2×D3—122no—
957C2×D3—122no—
958C2×D3—122no—
959C2×D3—122no—
960C2×D3—122no—
961C2×D3—122no—
962C2×D3—122no—
963C2×D3—122no—
964C2×D3—122no—
965C2×D3—122no—
966C2×D3—122no—
967C2×D3—122no—
968C3×C4—44no—
969C3×C4—42no—
970C3×C4—42no—
971C3×C4—64no—
972C3×C4—122no—
973C3×C4—122no—
974C3×C4—122no—
975Dic3—24no—
976Dic3—42no—
977Dic3—42no—
978Dic3—42no—
979Dic3—124no—
980Dic3—122no—
981Dic3—122no—
982C32#143911yescharacteristic, complemented, Sylow
983C23—94no—
984C23—182no—
985C23—182no—
986C23—182no—
987C23—182no—
988C23—182no—
989C23—182no—
990C23—182no—
991C23—182no—
992C23—182no—
993C23—182no—
994C23—182no—
995C23—182no—
996C23—182no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—182no—
1001C23—182no—
1002C23—361no—
1003C23—361no—
1004C23—361no—
1005C23—361no—
1006C23—361no—
1007C23—361no—
1008C23—361no—
1009C23—361no—
1010C23—361no—
1011C23—361no—
1012C23—361no—
1013C23—361no—
1014C23—361no—
1015C23—361no—
1016C23—361no—
1017C23—361no—
1018C23#379611yescharacteristic
1019C23#379711yescharacteristic
1020C23#379811yescharacteristic
1021C23#379911yescharacteristic
1022C23#379911yescharacteristic
1023C23#379911yescharacteristic
1024C23C4×D3211yescharacteristic
1025C23D3×D1211yescharacteristic
1026C23#380411yescharacteristic
1027C23C2×#62611yescharacteristic
1028C23D3×#6711yescharacteristic
1029C23D3×#6711yescharacteristic
1030C23D3×#6711yescharacteristic
1031C23#381111yescharacteristic
1032C23#381111yescharacteristic
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—34no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—182no—
1069C2×C4—182no—
1070C2×C4—182no—
1071C2×C4—361no—
1072C2×C4—361no—
1073C2×C4—361no—
1074C2×C4—361no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—21no—
1090C2×C3#466511yescharacteristic
1091C2×C3#466711yescharacteristic
1092C2×C3#466811yescharacteristic
1093C2×C3#466911yescharacteristic
1094C2×C3#467211yescharacteristic
1095C2×C3#467311yescharacteristic
1096C2×C3#467511yescharacteristic
1097C2×C3#467611yescharacteristic
1098C2×C3#494011yescharacteristic
1099C2×C3#495711yescharacteristic
1100C2×C3#495911yescharacteristic
1101C2×C3#496011yescharacteristic
1102C2×C3#498711yescharacteristic
1103C2×C3#498811yescharacteristic
1104C2×C3#498911yescharacteristic
1105C2×C3#498911yescharacteristic
1106C2×C3#498911yescharacteristic
1107C2×C3#499011yescharacteristic
1108C2×C3#499011yescharacteristic
1109C2×C3#499111yescharacteristic
1110C2×C3#499111yescharacteristic
1111C2×C3#499211yescharacteristic
1112C2×C3#499311yescharacteristic
1113C2×C3#499311yescharacteristic
1114C2×C3#499411yescharacteristic
1115C2×C3#499411yescharacteristic
1116C2×C3#499411yescharacteristic
1117C2×C3#521311yescharacteristic
1118C2×C3#522311yescharacteristic
1119C2×C3#523111yescharacteristic
1120D3—128no—
1121D3—124no—
1122D3—124no—
1123C22—184no—
1124C22—184no—
1125C22—184no—
1126C22—362no—
1127C22—362no—
1128C22—362no—
1129C22—362no—
1130C22—362no—
1131C22—362no—
1132C22—362no—
1133C22—362no—
1134C22—362no—
1135C22—362no—
1136C22—362no—
1137C22—362no—
1138C22#6383611yescharacteristic
1139C22#6384811yescharacteristic
1140C22#6385011yescharacteristic
1141C22#6385011yescharacteristic
1142C22#6385311yescharacteristic
1143C22#6386411yescharacteristic
1144C22#6386511yescharacteristic
1145C22#6386811yescharacteristic
1146C22#6387111yescharacteristic
1147C22#6388111yescharacteristic
1148C22#6388311yescharacteristic
1149C22#6388611yescharacteristic
1150C22#6388811yescharacteristic
1151C22#6388811yescharacteristic
1152C22#6388811yescharacteristic
1153C22#6389511yescharacteristic
1154C22#6389711yescharacteristic
1155C22#6389711yescharacteristic
1156C22C4×#62611yescharacteristic
1157C22#6390411yescharacteristic
1158C22#6390411yescharacteristic
1159C22#6390611yescharacteristic
1160C22#6390711yescharacteristic
1161C22#6390711yescharacteristic
1162C22#6390911yescharacteristic
1163C22#6391011yescharacteristic
1164C22#6391011yescharacteristic
1165C22D3×(C2×D3)⋊C411yescharacteristic
1166C22#6395811yescharacteristic
1167C22#6397111yescharacteristic
1168C22#6397711yescharacteristic
1169C22#6397811yescharacteristic
1170C22#6397911yescharacteristic
1171C22#6398111yescharacteristic
1172C22#6398311yescharacteristic
1173C4—42no—
1174C4—64no—
1175C4—122no—
1176C4—122no—
1177C4—122no—
1178C4—362no—
1179C3—21no—
1180C3#6942811yescharacteristic, complemented
1181C3#7157011yescharacteristic, complemented
1182C2—364no—
1183C2#1059120311yescharacteristic
1184C2#1059120411yescharacteristic
1185C2#1059125811yescharacteristic
1186C2#1059128911yescharacteristic
1187C2#1059129011yescharacteristic
1188C2#1059129111yescharacteristic
1189C2#1059131011yescharacteristic
1190C2#1059131111yescharacteristic
1191C2#1059132111yescharacteristic
1192C2#1059134711yescharacteristic
1193C2#1059136711yescharacteristic
1194C2#1059137411yescharacteristic
1195C2#1059138211yescharacteristic
1196C2#1059138411yescharacteristic
1197C2#1059172411yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
28. C2×#3722C4semidirect
40. C22×Dic3⋊C4D3semidirect
46. C2×C3⋊#95D3semidirect
209. C22×C3⋊D3C4⋊C4semidirect
251. C2×C3×Dic3C22⋊C4semidirect
739. C2×Dic3(C2×D3)⋊C4semidirect
982. C32#1439semidirect
1180. C3#69428semidirect
1181. C3#71570semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#37522
C22×C3×Dic3⋊C42
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#715703
#694283